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Among the properties describing the behavior of centrality measures with respect to network modifications, score monotonicity means that adding an arc increases the centrality score of the target of the arc; rank monotonicity means that adding an arc improves the importance of the target with respect to the remaining nodes. It is known (Boldi and Vigna Intern Math 10:222–262, 2014, Boldi et al. Netw Sci 5(4):529–550, 2017) that score and rank monotonicity hold in directed graphs for almost all the classical centrality measures. In undirected graphs one expects that the corresponding properties hold when adding a new edge—in this case, both endpoints of the new edge should enjoy the increase in score/rank. However, recent results (Boldi et al. in Netw Sci 11(3):1–23, 2023) have shown that this is not true: for many centrality measures, it is possible to find situations in which adding an edge reduces the rank of one of its two endpoints. In this paper we introduce a weaker property for undirected networks, semi-monotonicity, in which just one of the two endpoints of a new edge is required to enjoy score or rank monotonicity. We show that this property is satisfied by closeness centrality, by a large class of distance-based centralities, and (somehow surprisingly) by betweenness centrality. In the last two cases, we prove in fact a stronger property, basin dominance, which is of independent interest. [ABSTRACT FROM AUTHOR]

Let H be a complete r-uniform hypergraph such that two vertices are marked in each edge as its 'boundary' vertices. A linear ordering of the vertex set of H is called an agreeing linear order, provided all vertices of each edge of H lie between its two boundary vertices. We prove the following Helly-type theorem: if there is an agreeing linear order on the vertex set of every subhypergraph of H with at most 2r − 2 vertices, then there is an agreeing linear order on the vertex set of H. We also show that the constant 2r − 2 cannot be reduced in the theorem. The case r = 3 of the theorem has particular interest in the axiomatic theory of betweenness. Similar results are obtained for further r-uniform hypergraphs (r ≥ 3), where one or two vertices are marked in each edge, and the linear orders need to satisfy various rules of agreement. In one of the cases we prove that no such Helly-type statement holds. [ABSTRACT FROM AUTHOR]

Sustainable urban form research brought with it a renewed interest in neighborhood planning units (NPUs). While there is some insightful historical and qualitative research on the location of nonresidential uses in NPUs, quantitative analysis of the accessibility of nonresidential uses in NPUs has received minimal attention. This article uses Multiple Centrality Assessment to understand the accessibility of nonresidential land uses in NPUs designs. Using NPUs in Abu Dhabi as a case study, the paper analyzes different patterns of street networks across different scales and proposes new concepts and models for understanding accessibility. A framework for accessible NPUs focuses on three elements: street layout design, permeability, and edge attractiveness. Permeability is defined by high levels of Gravity and/or Betweenness at an NPU's center at a global scale. On the other hand, the edge attractiveness that provides strong "seams" between NPUs is defined by high values of Gravity and/or Betweenness at an NPU's edges and perimeter locations at a global scale. Findings suggest that a well-designed NPU must be characterized by both permeability and edge attractiveness. Results also indicate that nonresidential areas should be located according to their functions and level of intensity. Findings stress that at a local scale, NPUs should be designed to have high accessibility and low permeability for daily nonresidential facilities at the center. However, to promote the interconnection between adjacent NPUs, the street networks should have high accessibility and high edge attractiveness for nonresidential facilities located along the edges at a global scale. This research presents a conceptual approach and practical implications for planning NPUs' nonresidential land uses and it contributes to the debate and practice on accessibility in an NPU. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Japanese philosopher Tetsurō Watsuji's phenomenology of aidagara ("betweenness") and use his analysis in the contemporary context of online space. We argue that Watsuji develops a prescient analysis anticipating modern technologically-mediated forms of expression and engagement. More precisely, we show that instead of adopting a traditional phenomenological focus on face-to-face interaction, Watsuji argues that communication technologies—which now include Internet-enabled technologies and spaces—are expressive vehicles enabling new forms of emotional expression, shared experiences, and modes of betweenness that would be otherwise inaccessible. Using Watsuji's phenomenological analysis, we argue that the Internet is not simply a sophisticated form of communication technology that expresses our subjective spatiality (although it is), but that it actually gives rise to new forms of subjective spatiality itself. We conclude with an exploration of how certain aspects of our online interconnections are hidden from lay users in ways that have significant political and ethical implications. [ABSTRACT FROM AUTHOR]

Distance labeling approaches are widely adopted to speed up the online performance of shortest-distance queries. The construction of the distance labeling, however, can be exhaustive, especially on big graphs. For a major category of large graphs, small-world networks, the state-of-the-art approach is pruned landmark labeling (PLL ). PLL prunes distance labels based on a node order and directly constructs the pruned labels by performing breadth-first searches in the node order. The pruning technique, as well as the index construction, has a strong sequential nature which hinders PLL from being parallelized. It becomes an urgent issue on massive small-world networks whose index can hardly be constructed by a single thread within a reasonable time. This paper first scales distance labeling on small-world networks by proposing a parallel shortest-distance labeling (PSL ) scheme. PSL insightfully converts the PLL 's node-order dependency to a shortest-distance dependence, which leads to a propagation-based parallel labeling in D rounds where D denotes the diameter of the graph. To further scale up PSL , it is critical to reduce the index size. This paper proposes effective index compression techniques based on graph properties as well as label properties; it also explores best practices in using betweenness-based node order to reduce the index size. The efficient betweenness estimation of the graph nodes proposed may be of independent interest to graph practitioners. Extensive experimental results verify our efficiency on billion-scale graphs, near-linear speedup in a multi-core environment, and up to 94 % reduction in the index size. [ABSTRACT FROM AUTHOR]

Analyzing ego networks to investigate local properties and behaviors of individuals is a fundamental task in social network research. In this paper we show that there is not a unique way of defining ego networks when the existence of edges is uncertain, since there are two different ways of defining the neighborhood of a node in such network models. Therefore, we introduce two definitions of probabilistic ego networks, called V-Alters-Ego and F-Alters-Ego, both rooted in the literature. Following that, we investigate three fundamental measures (degree, betweenness and closeness) for each definition. We also propose a method to approximate betweenness of an ego node among the neighbors which are connected via shortest paths with length 2. We show that this approximation method is faster to compute and it has high correlation with ego betweenness under the V-Alters-Ego definition in many datasets. Therefore, it can be a reasonable alternative to represent the extent to which a node plays the role of an intermediate node among its neighbors. [ABSTRACT FROM AUTHOR]

Predicting how changes to the urban environment layout will affect the spatial distribution of pedestrian flows is important for environmental, social and economic sustainability. We present longitudinal evaluation of a model of the effect of urban environmental layout change in a city centre (Cardiff 2007–2010), on pedestrian flows. Our model can be classed as regression based direct demand using Multiple Hybrid Spatial Design Network Analysis (MH-sDNA) assignment, which bridges the gap between direct demand models, facility-based activity estimation and spatial network analysis (which can also be conceived as a pedestrian route assignment based direct demand model). Multiple theoretical flows are computed based on retail floor area: everywhere to shops, shop to shop, railway stations to shops and parking to shops. Route assignment, in contrast to the usual approach of shortest path only, is based on a hybrid of shortest path and least directional change (most direct) with a degree of randomization. The calibration process determines a suitable balance of theoretical flows to best match observed pedestrian flows, using generalized cross-validation to prevent overfit. Validation shows that the model successfully predicts the effect of layout change on flows of up to approx. 8000 pedestrians per hour based on counts spanning a 1 km2 city centre, calibrated on 2007 data and validated to 2010 and 2011. This is the first time, to our knowledge, that a pedestrian flow model with assignment has been evaluated for its ability to forecast the effect of urban layout changes over time. [ABSTRACT FROM AUTHOR]

Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph. [ABSTRACT FROM AUTHOR]

This paper shows that expected utility belongs to the intersection of models satisfying betweenness and a homotheticity condition for risky choice. Betweenness models can accommodate variable risk attitudes, originally highlighted by the Allais paradox, by restricting indifference curves to be linear while allowing non-parallelism. Homotheticity, in contrast, restricts indifference curves to be parallel while permitting non-linearities, such as those highlighted by inverse-S probability weighting. Data from an experiment indicate that approximately 2/3s of participants satisfied homotheticity. Of this group, about half satisfied the expected utility hypothesis. The other half violated expected utility and therefore betweenness. These results indicate that homothetic preferences, and in particular those violating betweenness, can be empirically relevant for decision making under risk. [ABSTRACT FROM AUTHOR]

Structural and functional approaches to the determination of vulnerability of complex network structures and systems to negative internal and external influences are considered. The concept of parameters of influence and betweenness of system elements is introduced, which allows us to identify the most important from the functional point of view nodes and edges of the network and develop scenarios for identifying those components of the system whose blocking can cause greatest losses in the process of its functioning, and also quantify these losses. The sensitivity of the system to small variations in the volume of flow movement, which are close to the critical loading of its components, is analyzed. The obtained results can be used to improve the available methods and develop new ones to protect real network systems from various natural and artificial damages. [ABSTRACT FROM AUTHOR]

The notions of betweenness centrality (BC) and group betweenness centrality (GBC) are widely used in social network analyses. We introduce variants of them; namely, the k-step BC and k-step GBC. The k-step GBC of a group of vertices in a network is a measure of the likelihood that at least one group member will get the information communicated between pairs of vertices through shortest paths within the first k steps of the start of the communication. The k-step GBC of a single vertex is the k-step BC of that vertex. The introduced centrality measures may find uses in applications where it is important or critical to obtain the information within a fixed time of the start of the communication. For the introduced centrality measures, we propose an algorithm that can compute successively the k-step GBC of several groups of vertices. The performance of the proposed algorithm is evaluated through computational experiments. The use of the new BC measures leads to an earlier control of the information (virus, malware, or rumor) before it spreads through the network. [ABSTRACT FROM AUTHOR]

Traffic network is basically a "network of networks" consisting of mainly two types of networks: road network and a travel network. Due to drastic increase in population of vehicles, traffic congestion in metro cities of India is a severe problem. To resolve this use, we have proposed an approach to dynamic and automatic road traffic light management system. The approach is based on arithmetic mean theorem. The input to the control interface of traffic light of proposed approach are six different parameters : velocity of traffic units (v), queue length (l), inter-arrival time between vehicles (t), centrality measures value(c) and predicted value (prdt v) of traffic congestion by historical database and output is level of congestion. On the basis of congestion level, we build inference rules. The proposed approach automatically updates duration of green and red light as per the level of congestion at a particular junction. Proposed approach follows forward reasoning of If–Then rules. A study of this approach is done in this paper on various traffic situations of Delhi, India depending on queue length of vehicles. [ABSTRACT FROM AUTHOR]

Big data involves a large amount of data generation, storage, transfer from one place to another, and analysis to extract meaningful information. Information centric networking (ICN) is an infrastructure that transfers big data from one node to another node, and provides in-network caches. For software defined network-based ICN approach, a recently proposed centralized cache server architecture deploys single cache server based on path-stretch value. Despite the advantages of centralized cache in ICN, single cache server for a large network has scalability issue. Moreover, it only considers the path-stretch ratio for cache server deployment. Consequently, the traffic can not be reduced optimally. To resolve such issues, we propose to deploy multiple cache servers based on joint optimization of multiple parameters, namely: (i) closeness centrality; (ii) betweenness centrality; (iii) path-stretch values; and (iv) load balancing in the network. Our proposed approach first computes the locations and the number of cache servers based on the network topology information in an offline manner and the cache servers are placed at their corresponding locations in the network. Next, the controller installs flow rules at the switches such that the switches can forward the request for content to one of its nearest cache server. Upon reaching a content request, if the content request matches with the contents stored at the cache server, the content is delivered to the requesting node; otherwise, the request is forwarded to the controller. In the next step, controller computes the path such that the content provider first sends the content to the cache server. Finally, a copy of the content is forwarded to the requesting node. Simulation results confirmed that the proposed approach performs better in terms of traffic overhead and average end-to-end delay as compared to an existing state-of-the-art approach. [ABSTRACT FROM AUTHOR]

The pursuit-evasion game with two persons is considered. Both players are moving in a metric space, have equal maximum speeds and complete information about the location of each other. We study the sufficient conditions for a capture (with a positive capture radius). We assume that Lion wins if he manages the capture independently of the initial positions of the players and the evader's strategy. We prove that the discrete-time simple pursuit strategy is a Lion's winning strategy in a compact geodesic space satisfying the betweenness property. In particular, it means that Lion wins in compact CAT(0)-spaces, Ptolemy spaces, Buseman convex spaces, or any geodesic space with convex metric. We also do not need to use such properties as finite dimension, smoothness, boundary regularity, or contractibility of the loops. [ABSTRACT FROM AUTHOR]

Many complex systems in the real world such as social networks can be modeled by complex networks. The complex network analysis and especially community detection is an important research topic in graph analysis that aims to identify the structure of a graph and its similar groups of nodes. In recent years, various algorithms such as Girvan and Newman's method (GN) is introduced which is based on a divisive approach for graph clustering. Although GN is a highly popular and widely used method, it suffers from scalability and computational complexity. GN needs O(m3) and O(m3 + m3logm) time to detects communities in unweighted and weighted graphs respectively. Hence, in this paper, a faster method is suggested that detects communities in O(m2) for both weighted and unweighted graphs. In this paper, firstly, we define degree for each edge and then we propose a new and fast approach for the calculation of edges betweenness that is based on edge degree centrality. Furthermore, in order to boost the speed of the algorithm, we suggest instead of just one edge, multiple edges can be removed in each iteration. Since the proposed method wants to enhance the GN method, in the evaluation section the quality of detected communities, the accuracy and speed of the suggested method are assessed by the comparison with the GN method. Results prove that our proposed method is extremely faster than plain GN and the detected communities often have better quality than the plain GN method. Furthermore, we compare our proposed method with meta-heuristic algorithms which are a novel approach for community detection. Results clarify that the suggested method is notably faster, scalable, stable, reliable, and efficient than meta-heuristic algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we presents a new method for extracting interest points from RGB images by complex network analysis theory. Firstly, the RGB images are expressed as the multi-level complex network model. The nodes in the complex network model are the maximum degree pixel of subgraphs and the links are the similarity and distance between the maximum degree pixels. Then three different algorithms were proposed to locate these interest points based on three topology features of high-level complex network model, which are degree, closeness and betweenness centrality. In order to verify the effectiveness of our algorithm, we use our algorithm for four different test images. It is remarkable that the identify targets by degree centrality algorithm are similar to Harris and SIFT algorithm, and the accuracy are more than them. The results show that our algorithm could identify interest points from the images effectively. [ABSTRACT FROM AUTHOR]

In decision theory, the betweenness axiom postulates that a decision maker who chooses an alternative A over another alternative B must also choose any probability mixture of A and B over B itself and can never choose a probability mixture of A and B over A itself. The betweenness axiom is a weaker version of the independence axiom of expected utility theory. Numerous empirical studies documented systematic violations of the betweenness axiom in revealed individual choice under uncertainty. This paper shows that these systematic violations can be linked to another behavioral regularity—choice shifts in a group decision making. Choice shifts are observed if an individual faces the same decision problem but makes a different choice when deciding alone and in a group. [ABSTRACT FROM AUTHOR]

This study measures severity of network disruptions in the Minneapolis-St. Paul region by comparing the cumulative opportunity accessibility before-and-after removing freeway segments. Accessibility to jobs and accessibility to resident workers are measured respectively in the morning and evening peak hours. It is shown that the links with more severe consequences of disruption tend to be near or at freeway interchanges. Betweenness helps explain risk severity. [ABSTRACT FROM AUTHOR]

Given finitely many events in a probability space, conditional independences among the indicators of events are considered simultaneously with the signs of covariances. Resulting discrete structures are studied restricting attention mostly to all couples and triples of events. Necessary and sufficient conditions for such structures to be represented by events are found. Consequences of the results for the patterns of conjunctive forks are discussed. [ABSTRACT FROM AUTHOR]

Word sense disambiguation (WSD) refers to the task of finding the intended meaning of a word in a given sentence. WordNet® (lexical database based on psychological principals) based on WSD methods have been discussed extensively. WordNet® relates words through various relations and all the WSD approaches available in the literature till date rely on the notion of assigning equal importance to each relation. But actually in real-world situations, these relations do not exhibit equal importance, so they should not be given equal weight. The paper presents a novel method for exploiting the idea of WordNet® relations weight based on its importance and thus assigns the weights to the edges of the WordNet® graph, µ ∊  (0, 1]. This helps in fuzzifying the WordNet® graph, where nodes represent the words and weighted edges represent the relation of the words with strength∈ (0,1]. The values for edge weight assignment are obtained using test cases based on a simulated annealing method. The proposed method utilizes various Fuzzy graph connectivity measures to determine the significance of each node in the Fuzzy graph, resulting in identification of the intended meaning of the word. This method is tested on the SemCor dataset and observed that it gives better results when compared to state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

Journals were central to Eugene Garfield’s research interests. Among other things, journals are considered as units of analysis for bibliographic databases such as the Web of Science and Scopus. In addition to providing a basis for disciplinary classifications of journals, journal citation patterns span networks across boundaries to variable extents. Using betweenness centrality (BC) and diversity, we elaborate on the question of how to distinguish and rank journals in terms of interdisciplinarity. Interdisciplinarity, however, is difficult to operationalize in the absence of an operational definition of disciplines; the diversity of a unit of analysis is sample-dependent. BC can be considered as a measure of multi-disciplinarity. Diversity of co-citation in a citing document has been considered as an indicator of knowledge integration, but an author can also generate trans-disciplinary—that is, non-disciplined—variation by citing sources from other disciplines. Diversity in the bibliographic coupling among citing documents can analogously be considered as diffusion  or differentiation of knowledge across disciplines. Because the citation networks in the cited direction reflect both structure and variation, diversity in this direction is perhaps the best available measure of interdisciplinarity at the journal level. Furthermore, diversity is based on a summation and can therefore be decomposed; differences among (sub)sets can be tested for statistical significance. In the appendix, a general-purpose routine for measuring diversity in networks is provided. [ABSTRACT FROM AUTHOR]

We give a non-Paschian plane based on the property of betweenness which cannot be derived from an ordering of the points of a line. In this model there is no possibility to define the congruence of segments but we can define angle, triangle and angle measure, respectively. With respect to our definitions the plane has an elliptic character, meaning that the sum of the angles of a triangle is greater than $${\pi}$$ . [ABSTRACT FROM AUTHOR]

Community structures and relation patterns, and ranking them for social networks provide us with great knowledge about network. Such knowledge can be utilized for target marketing or grouping similar, yet distinct, nodes. The ever-growing variety of social networks necessitates detection of minute and scattered communities, which are important problems across different research fields including biology, social studies, physics, etc. Existing community detection algorithms such as fast and folding or modularity based are either incapable of finding graph anomalies or too slow and impractical for large graphs. The main contributions of this work are twofold: (i) we optimize the Attractor algorithm, speeding it up by a factor depending on complexity of the graph; i.e. the more complex a social graph is, the better result the algorithm will achieve, and (ii) we propose a community ranker algorithm for the first time. The former is achieved by amalgamating loops and incorporating breadth-first search (BFS) algorithm for edge alignments and to fill in the missing cache, preserving a constant of time equal to the number of edges in the graph. For the latter, we make the first attempt to enumerate how influential each community is in a given graph, ranking them based on their normalized impact factor. [ABSTRACT FROM AUTHOR]

Models of science address statistical properties and mechanisms of science. From the perspective of scholarly information retrieval (IR) science models may provide some potential to improve retrieval quality when operationalized as specific search strategies or used for rankings. From the science modeling perspective, on the other hand, scholarly IR can play the role of a validation model of science models. The paper studies the applicability and usefulness of two particular science models for re-ranking search results (Bradfordizing and author centrality). The paper provides a preliminary evaluation study that demonstrates the benefits of using science model driven ranking techniques, but also how different the quality of search results can be if different conceptualizations of science are used for ranking. [ABSTRACT FROM AUTHOR]

Contingency analysis is important for providing information about the vulnerability of power grids. Many methods have been purposed to use topological structures of power grids for analyzing contingency states. Considering failures of buses and lines, we present and compare several graph methods for selecting contingencies in this paper. A new method, called critical node detection, is introduced for selecting contingencies consisting of failures on buses. Besides these methods, we include an interdiction model which provides the worst case contingency selection. Our measurement for contingency evaluation is to maximize the social benefit, or to minimize the generating and load shedding cost. Comparing with other measurements for contingency selection, our model is based on economic analysis and is reasonable for evaluating the selected contingency state. Additionally, a contingency consisting of both buses and lines is also studied. [ABSTRACT FROM AUTHOR]

An adaptive predictive pinning control is proposed to suppress the cascade in coupled map lattices (CMLs). Two monitoring strategies are applied: (1) A specific fraction of nodes with the highest degree or betweenness are chosen to constitute the set of monitored nodes; (2) During the cascade, an adaptive pinning control is implemented, in which only the nodes in the monitored set whose current state is normal but whose predictive state is abnormal, are pinned with the predictive controller. Simulations show that for the scale-free (SF) CML the degree-based monitoring strategy is advantageous over the betweenness-based strategy, while for the small-world (SW) CML the situation is the opposite. With the adaptive predictive pinning control, the fewer local controllers can effectively suppress the cascade throughout the whole network. [ABSTRACT FROM AUTHOR]

Maintaining symbiotic inter-relationships with suppliers is an integral part of developing tightly interwoven vertical supply arrangements among members participating in a network of companies. This article reviews the relevant literature on network theory to test the interrelationships among transactions, cross shareholdings, and sales among all the firms in Mazda's Yokokai Keiretsu. Rooted in graph theory, the degree of betweenness, cross shareholdings, and closeness indicators were used to compute the centrality index, which was then employed to explore the nature of the relationship between transactions and sales, as well as that between cross shareholdings and sales. The findings reveal statistically significant inter-correlations between transactions and sales, and between cross shareholdings and sales. Managerial implications are discussed and conclusions are presented. [ABSTRACT FROM AUTHOR]

We study global and local Q-measures, as well as betweenness centrality, as indicators of international collaboration in research. After a brief review of their definitions, we introduce the concepts of external and internal inter-group geodesics. These concepts are applied to a collaboration network of 1129 researchers from different countries, which is based on publications in bibliometrics, informetrics, webometrics, and scientometrics (BIWS in short) from the period 1990-2009. It is thus illustrated how international collaboration (among authors from different countries) in BIWS is carried out. Our results suggest that average scores for local Q-measures are typically higher, indicating a relatively low degree of international collaboration in BIWS. The dominating form of international collaboration is bilateral, whereas multilateral collaboration is relatively rare in the field of BIWS. We also identify and visualize the most important global and local actors. Dividing the entire period in four 5-year periods, it is found that most international collaboration in the field has happened in the last time slice (2005-2009). A comparison of the different time slices reveals the non-linear growth of the indicators studied and the international expansion of the field. [ABSTRACT FROM AUTHOR]

For a finite poset P = ( V, ≤ ), let ${\cal B}_s(P)$ consist of all triples ( x, y, z) ∈ V such that either x < y < z or z < y < x. Similarly, for every finite, simple, and undirected graph G = ( V, E), let ${\cal B}_s(G)$ consist of all triples ( x, y, z) ∈ V such that y is an internal vertex on an induced path in G between x and z. The ternary relations ${\cal B}_s(P)$ and ${\cal B}_s(G)$ are well-known examples of so-called strict betweennesses. We characterize the pairs ( P, G) of posets P and graphs G on the same ground set V which induce the same strict betweenness relation ${\cal B}_s(P)={\cal B}_s(G)$. [ABSTRACT FROM AUTHOR]

Centrality of an edge of a graph is proposed to be viewed as a degree of global sensitivity of a graph distance function (i.e., a graph metric) on the weight of the considered edge. For different choices of distance function, contact is made with several previous ideas of centrality, whence their different characteristics are clarified, and strengths or short-comings are indicated, via selected examples. The centrality based on “resistance distance” exhibits several nice features, and might be termed “amongness” centrality. [ABSTRACT FROM AUTHOR]

The Hausdoff metric h was introduced by Felix Hausdoff in the early 20th century as a way to measure the distance between elements in the hyperspace $${\mathcal{H}}({\mathbb{R}}^{n})$$ of non-empty compact subsets of $${\mathbb{R}}^{n}$$. The geometry this metric imposes on $${\mathcal{H}}({\mathbb{R}}^{n})$$ has many interesting properties: lines in this geometry can have endpoints; there can be many elements at a given location between two sets in $${\mathcal{H}}({\mathbb{R}}^{n})$$; the Fibonacci and Lucas numbers arise in a natural way in this geometry; and for infinitely many different values of the positive integer k, there is a configuration [ A, B] in $${\mathbb{R}}^{n}$$ so that there exist exactly k elements at each location between A and B. In this paper we will show that if k is between 1 and 18, there is always a configuration having exactly k elements at each location between the end elements and prove the surprising result that no such configuration exists if k equals 19. [ABSTRACT FROM AUTHOR]

By considering the flow control of urban sewer networks to minimize the electricity consumption of pumping stations, a decomposition-coordination strategy for energy savings based on network community division is developed in this paper. A mathematical model characterizing the steady-state flow of urban sewer networks is first constructed, consisting of a set of algebraic equations with the structure transportation capacities captured as constraints. Since the sewer networks have no apparent natural hierarchical structure in general, it is very difficult to identify the clustered groups. A fast network division approach through calculating the betweenness of each edge is successfully applied to identify the groups and a sewer network with arbitrary configuration could be then decomposed into subnetworks. By integrating the coupling constraints of the subnetworks, the original problem is separated into N optimization subproblems in accordance with the network decomposition. Each subproblem is solved locally and the solutions to the subproblems are coordinated to form an appropriate global solution. Finally, an application to a specified large-scale sewer network is also investigated to demonstrate the validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In binary choice between discrete outcome lotteries, an individual may prefer lottery L 1 to lottery L 2 when the probability that L 1 delivers a better outcome than L 2 is higher than the probability that L 2 delivers a better outcome than L 1. Such a preference can be rationalized by three standard axioms (solvability, convexity and symmetry) and one less standard axiom (a fanning-in). A preference for the most probable winner can be represented by a skew-symmetric bilinear utility function. Such a utility function has the structure of a regret theory when lottery outcomes are perceived as ordinal and the assumption of regret aversion is replaced with a preference for a win. The empirical evidence supporting the proposed system of axioms is discussed. [ABSTRACT FROM AUTHOR]

This article extends Karni's (1992) Utility Theory with Probability Dependent Outcome Valuation (UTPDOV) to accommodate a wider set of preferences, and applies the new representation to a variety of decision problems under risk. First, we present a new, more general, axiomatization of UTPDOV that renders the underlying intuition more transparent. Second, we develop sufficient conditions under which UTPDOV satisfies the betweenness and the ordinal independence axioms. Finally, we examine functional forms of the UTPDOV model that are consistent with several well known departures from the independence axiom. [ABSTRACT FROM AUTHOR]

Betweeness is a weakened form of the independence axiom, staling that a probability mixture of two gambles should lie between them in preference. Betweenness is used in many generalizations of expected utility and in applications to game theory and macroeconomics. Experimental violations of betweenness are widespread. We rule out intransitivity as a source of violations and find that violations are less systematic when mixtures are presented in compound form (because the compound lottery reduction axiom fails empirically). We also fit data from nine studies using Gul's disappointment-aversion theory and two variants of EU, which weight separate or cumulative probabilities nonlinearly. The three theories add only one parameter to EU and fit much better. [ABSTRACT FROM AUTHOR]

Analyzing ego networks to investigate local properties and behaviors of individuals is a fundamental task in social network research. In this paper we show that there is not a unique way of defining ego networks when the existence of edges is uncertain, since there are two different ways of defining the neighborhood of a node in such network models. Therefore, we introduce two definitions of probabilistic ego networks, called V-Alters-Ego and F-Alters-Ego, both rooted in the literature. Following that, we investigate three fundamental measures (degree, betweenness and closeness) for each definition. We also propose a method to approximate betweenness of an ego node among the neighbors which are connected via shortest paths with length 2. We show that this approximation method is faster to compute and it has high correlation with ego betweenness under the V-Alters-Ego definition in many datasets. Therefore, it can be a reasonable alternative to represent the extent to which a node plays the role of an intermediate node among its neighbors. [ABSTRACT FROM AUTHOR]